What is the average rate of change from x = −1 to x = −2?

Hi !

Can you provide the function?

from this

vertex is (1, 5) & y-intercept is (0, 7)

So

We just substitute as before into the vertex form of our quadratic function.

We have (h, k) = (-1, 5) and at x = 0, y = 7.

y = a(x - h)^2 + k

Now

7 = a(0 - (-1))^2 + 5

7 = a(1)^2 + 5

7 - 5 = a(1)

2 = a

Now the function is

f(x) = 2(x −(−1))^2 + 5

f(x) = 2(x + 1)^2 + 5

f(x) = 2(x^2 + 1 + 2x) + 5

f(x) = 2x^2 + 4 + 4x + 5

f(x) = 2x^2 + 4x + 9

f(-1) = 7 f(-2) = 9

x1 = -1 x2 = - 2

Then the average rate of change is

=

= - 2

OPTION 2 is right.

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